KABUL, Afghanistan (AP) — Former Afghan Foreign Minister Abdullah Abdullah’s lead slightly increased in partial results for Afghanistan’s presidential election released Sunday, but he and rival Ashraf Ghani Ahmadzai still seem to be heading for a runoff next month.

The winner will replace Hamid Karzai, the only president the country has known since the 2001 US-led invasion ousted the Taliban, and will oversee a tumultuous period as the US and NATO are expected to withdraw most of their troops from the country by the end of this year. Karzai, whose relations with Washington have sharply deteriorated, was constitutionally barred from running for a third term.

The latest numbers showed Abdullah with 44 percent of the vote tallied so far. Ahmadzai, a former finance minister and World Bank official, received 33.2 percent in the partial results. Zalmai Rassoul, another ex-foreign minister, had 10.4 percent. Final results aren’t due until May 14.

Both Abdullah and Ahmadzai have promised a fresh start with the West and have vowed to move ahead a security pact with the US that Karzai has refused to sign. That pact would allow a small force of American soldiers to stay in the country to continue training Afghan army and police to fight the Taliban.

The results announced by Ahmad Yousuf Nouristani, the chairman of Afghanistan’s Independent Election Commission, represent about half of the estimated 7 million ballots cast in the April 5 poll.

After the announcement, Abdullah said he still thinks it’s possible for him to win more than 50 percent of the vote to avoid the runoff.

“For us, we will accept the outcome of a fair and transparent process. Anything short of that will be problematic,” he told The Associated Press. “It’s important that the process is a free and fair one. That is important. Then if it goes to the second round in accordance to the rule of law, we are ready for that as well. ”

The results were a slight improvement for Abdullah from the first results announced April 13. Then, he had 41.9 percent of the vote to Ahmadzai’s 36.7 percent.

Still, with millions of votes yet to be counted, the results could change. Both Ahmadzai and Abdullah’s campaigns insist that their internal tallies — based on their poll observers — give them a majority.

Ahmadzai’s campaign spokesman, Hamidullah Farooqi, said the partial results under-represent areas where his candidate has strong support.

“I think he is very hopeful to finish it in the first round,” Farooqi said of Ahmadzai. “But if not, he will accept the law and respect that and we will go for a runoff.”

Abdullah was the runner-up to Karzai during the 2009 vote which was marred by widespread allegations of fraud. He has drawn on his strong following among ethnic Tajiks in Afghanistan’s north but is perceived to be weak among the country’s largest ethnic group — the Pashtuns — even though he’s half-Pashtun.

The specter of fraud also hangs over this vote. There have been allegations of vote rigging, but officials say it’s too soon to know how it might affect results.

Copyright 2014 The Associated Press.